Mary does have great power because of her role in salvation given to her by God. She sits at the right hand of her son Jesus in heaven and is queen of heaven and of earth. She definitely has great weight before the throne of God.
Then why pray to the other saints? I can only answer for myself. I pray to them because I know something about their life, what they did, and admire them, and have learned something of their loving approach to God. And in my admiration, I spontaneiously begin to talk to them about the things that are in my life and ask help for what I see going on around me. A prayer to them just sort of happens. It is more of a conversation and then a request of them to pray for me is some special sort of way since they seem to have handled their situations well.
At other times there are special days the church honors them in the Mass and asks for their special help.
On other occasions there is a litany of saints, or a list of great saints, that is prayed on occasions by the church or by anyone that they ask God for assistance for us.
Here is one list, there are others.
The Risen Christ, be our hope
Name of Jesus, strengthen us
Blood of Jesus, purify us
Body of Jesus, feed us
Heart of Jesus, forgive us
Heart of Mary, remember us
…RESPONSE: pray for us
Our Lady of Fatima
Our Lady of Lourdes
Our Lady of the Rosary
Our Lady of Mount Carmel
Our Lady of Guadalupe
Our Lady of Grace
ST Joseph
ST Ann
ST Elizabeth
ST John the Baptist
ST Mary Magdelene
ST Bernadette
ST Catherine Laboure
ST Margaret Mary
ST Bridget
ST Faustina
ST Theresa Little Flower
ST Theresa of Avila
ST Catherine of Siena
ST Joan of Arc
ST Maria Garretti
Blessed mother Theresa
Blessed John the 23rd
Venerable Pious the 12th
ST Isaac Jocques
ST Francis
ST Anthony
ST Benedict
ST Bernard
ST Dominic
ST Patrick
ST Valentine
ST Nicholas
ST Vincent DePauw
ST Augustine
All you holy men and women in heaven
Archangel Rapheal, heal us
Archangel Gabriel, enliighten us
Archangel Michael, protect us
Guardian angels, help us
Angel of Fatima, bring us peace
All you choirs of angels, pray with us
ST Peter, pray for us
ST Paul
ST John
ST James
ST Andrew
ST Jude(Thaddeus)
ST Mathew
ST Bartholomew
ST Phillip
ST Thomas
ST James
ST Simon
All before the throne of God in heaven, in your compassion help us.